Extensions of Modules with ACC on d-annihilators  

作　　者：Ouyang Lun-qun Zhou Qiong Liu Jin-wang Xiang Yue-ming 

机构地区：[1]School of Mathematics, Hunan University of Science and Technology [2]Department of Mathematics and Applied Mathematics, Huaihua University

出　　处：《Communications in Mathematical Research》2018年第1期23-35,共13页数学研究通讯（英文版）

基　　金：The NSF(11471108) of China;the NSF(2015JJ2051,2016JJ2050) of Hunan Province;the Teaching Reform Foundation(G21316) of Hunan Province

摘　　要：A unitary right R-module MR satisfies acc on d-annihilators if for every sequence（a;）;of elements of R the ascending chain AnnM（a;）■ AnnM（a;a;）■AnnM（a;a;a;）■… of submodules of MR stabilizes. In this paper we first investigate some triangular matrix extensions of modules with acc on d-annihilators. Then we show that under some additional conditions,the Ore extension module M[x]R[x;α,δ]over the Ore extension ring R[x;α,δ] satisfies acc on d-annihilators if and only if the module MR satisfies acc on d-annihilators. Consequently, several known results regarding modules with acc on d-annihilators are extended to a more general setting.A unitary right R-module MR satisfies acc on d-annihilators if for every sequence(a_n)_n of elements of R the ascending chain AnnM(a_1)■ AnnM(a_1 a_2)■AnnM(a_1 a_2 a_3)■… of submodules of MR stabilizes. In this paper we first investigate some triangular matrix extensions of modules with acc on d-annihilators. Then we show that under some additional conditions,the Ore extension module M[x]R[x;α,δ]over the Ore extension ring R[x;α,δ] satisfies acc on d-annihilators if and only if the module MR satisfies acc on d-annihilators. Consequently, several known results regarding modules with acc on d-annihilators are extended to a more general setting.

关 键 词：triangular matrix extension Ore extension acc on d-annihilator 

分 类 号：O1[理学—数学]